14,572 research outputs found
Robust Multidimensional Poverty Comparisons
We investigate how to make poverty comparisons using multidimensional indicators of well-being, showing in particular how to check whether the comparisons are robust to the choice of poverty indices and poverty lines. Our methodology applies equally well to either of what can be defined as "union" and "intersection" approaches to dealing with multidimensional indicators of well-being. When one of two variables is discrete, our methods specialize to those that Atkinson (1991), Jenkins and Lambert (1993) and others have developed to deal with household composition heterogeneity. The results also extend the statistical results recently derived in Davidson and Duclos (2000) to cases where well-being is measured in two or more dimensions. We thus derive the sampling distribution of various multidimensional poverty estimators, including estimators of the "critical" frontiers of poverty lines above which multidimensional poverty comparisons are no longer ethically robust.Multidimensional Poverty, Stochastic Dominance
Polarization: Robust Multidimensional Poverty Comparisons
We investigate how to make poverty comparisons using multidimensional indicators of well-being, showing in particular how to check whether the comparisons are robust to aggregation procedures and to the choice of multidimensional poverty lines. In contrast to earlier work, our methodology applies equally well to what can be defined as "union", "intersection" or "intermediate" approaches to dealing with multidimensional indicators of well-being. When one of two indicators is discrete, our methods specialize to those that have previously been developed to deal with household composition heterogeneity. To make these procedures of some practical usefulness, the paper is also the first to derive the sampling distribution of various multidimensional poverty estimators, including estimators of the "critical" poverty frontiers outside which multidimensional poverty comparisons can no longer be deemed ethically robust. The results are illustrated using data from a number of developing countries.Multidimensional Poverty, Stochastic Dominance
Fast and robust curve skeletonization for real-world elongated objects
We consider the problem of extracting curve skeletons of three-dimensional,
elongated objects given a noisy surface, which has applications in agricultural
contexts such as extracting the branching structure of plants. We describe an
efficient and robust method based on breadth-first search that can determine
curve skeletons in these contexts. Our approach is capable of automatically
detecting junction points as well as spurious segments and loops. All of that
is accomplished with only one user-adjustable parameter. The run time of our
method ranges from hundreds of milliseconds to less than four seconds on large,
challenging datasets, which makes it appropriate for situations where real-time
decision making is needed. Experiments on synthetic models as well as on data
from real world objects, some of which were collected in challenging field
conditions, show that our approach compares favorably to classical thinning
algorithms as well as to recent contributions to the field.Comment: 47 pages; IEEE WACV 2018, main paper and supplementary materia
On multivariate quantiles under partial orders
This paper focuses on generalizing quantiles from the ordering point of view.
We propose the concept of partial quantiles, which are based on a given partial
order. We establish that partial quantiles are equivariant under
order-preserving transformations of the data, robust to outliers, characterize
the probability distribution if the partial order is sufficiently rich,
generalize the concept of efficient frontier, and can measure dispersion from
the partial order perspective. We also study several statistical aspects of
partial quantiles. We provide estimators, associated rates of convergence, and
asymptotic distributions that hold uniformly over a continuum of quantile
indices. Furthermore, we provide procedures that can restore monotonicity
properties that might have been disturbed by estimation error, establish
computational complexity bounds, and point out a concentration of measure
phenomenon (the latter under independence and the componentwise natural order).
Finally, we illustrate the concepts by discussing several theoretical examples
and simulations. Empirical applications to compare intake nutrients within
diets, to evaluate the performance of investment funds, and to study the impact
of policies on tobacco awareness are also presented to illustrate the concepts
and their use.Comment: Published in at http://dx.doi.org/10.1214/10-AOS863 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Discrete Symmetries in the Weyl Expansion for Quantum Billiards
We consider two and three-dimensional quantum billiards with discrete
symmetries. We derive the first terms of the Weyl expansion for the level
density projected onto the irreducible representations of the symmetry group.
As an illustration the method is applied to the icosahedral billiard. The paper
was published in J. Phys. A /27/ (1994) 4317-4323Comment: 8 printed pages Latex fil
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